Two things:

All the answers here assume digits cannot be repeated. Why? Does the question mention so?

The question states: "How many three-digit integers can be created from 5 distinct digits?"

If we assume five distinct digits to be {1,2,3,4,5}

Can't I create three digit integer "111" form the above set of numbers?

Per the question, 111 is a three-digit integer that "can be created" from the given set of numbers
Per the question, 112 is another three-digit integer that "can be created" from the given set of numbers.

And so on and so forth...

Maybe the author meant to say "How many 3 digit integers with distinct digits can be created from 5 distinct digits?"

So, if we assume 1,2,3,4,5 to be the 5 digits we get following 60 three digit integers with "distinct digits"

123 124 125 134 135 145 234 235 245 345
132 142 152 143 153 154 243 253 254 354
213 214 215 314 315 415 324 325 425 435
231 241 251 341 351 451 342 352 452 453
312 412 512 413 513 514 423 523 524 534
321 421 521 431 531 541 432 532 542 543

These could be the combinations that the author might have visualized. But to get these, question should have been modified to ensure digits are not repeated!!

But the problem does not end here!!!

What if "0" is a digit out of the 5 distinct digits?? For example: {0,1,2,3,4}

Here I cannot have 012, 013 etc. as three digit integers. So the number of possibilities will reduce further!

Isn't the question ambiguous?